Preheat your oven to 350℉. Line an 8x4 inch loaf pan with parchment paper.
To a blender or food processor, add the ingredients of the bread - EXCEPT the shredded carrot and walnuts. Pulse this until mostly smooth. Then stir in the carrot and walnuts with a spatula. Pour this mixture into your pan and bake for 35-40 minutes. Or until toothpick comes out clean. Let the bread set in the pan for 20 minutes then transfer to a cooling rack and allow to cool completely for the frosting.
Frosting:
Add all frosting ingredients to a small bowl and whisk until smooth. Spread the mixture on top of the cool loaf atop with some crushed walnuts.
Notes
Nutritional Info includes the Frosting!Store leftovers in your fridge in an airtight container.